# Calculating Variable Pulling Force on a Spring on an Arc

• mybrohshi5
In summary, the diabolical trainer set up an apparatus with a block that has a mass of 23 kg and a spring that has a negligible mass and force constant of 450 N/m. The trainee must maintain a variable pulling force which is always tangent to a nearly frictionless, semicircular surface. By slowly varying the force, the block is moved (at a very slow constant speed), and the spring is stretched from position 1 to position 2. The end of the spring moves in an arc of radius 49 cm.
mybrohshi5

## Homework Statement

As test of strength, a diabolical trainer sets up the following apparatus. The trainee must maintain a variable pulling force which is always tangent to a nearly frictionless, semicircular surface . By slowly varying the force, a block with mass 23.0 kg is moved (at a very slow constant speed), and the spring to which it is attached is stretched from position 1 to position 2 (through an angle of 36 degrees). The spring has negligible mass and force constant 450 N/m. The end of the spring moves in an arc of radius a~=~ 49.0 cm.

http://session.masteringphysics.com/problemAsset/1000054849/9/YF-07-41.jpg

What is the necessary size of the trainee's variable pulling force at position 2?

F=-kx

## The Attempt at a Solution

I found the length of the arc first

36/180 = .2

C = 2(pi)R(1/2)
C = 0.49(pi)

Arc = .2(.49*pi)
Arc = 0.307876 m

then i multiplied that by the spring force constant

F = 0.3079(450)

F = 138.5 N

I think this is wrong cause i am not taking the mass into consideration but i wasnt sure where or how to include the mass of the block.

Any suggestions?

Thank you

Suggestions

1. Work with symbols and plug in the numbers at the very end. It will be easier for you to see what's going on.
2. Draw a free body diagram of the block at position 2, put in all the forces and find the net force.
3. Use Newton's Second Law. What is the acceleration in this case?

2. Ok drew my free body diagram. I have weight going down, the normal force perpendicular to the surface of the arc, the pulling force in the same place as in the picture, and the force of the spring in the opposite direction of the pulling force.

2. I believe the net force would be ZERO because it is being pulled at a constant speed and is not accelerating therefore giving it a net force of zero.

3. wouldn't the acceleration be zero because its being pulled at a constant speed?

Would i find the sum of the forces in the x and y directions and then find the resultant force and that will be my trainee's variable pulling force at position 2?

I got it. Thank you :)

## 1. What is a force-spring on an arc?

A force-spring on an arc is a type of physical system that consists of a spring attached to a rotating arc. The spring is typically anchored at one end and connected to a mass at the other end. When the arc is rotated, the spring stretches or compresses, generating a force on the mass.

## 2. How does a force-spring on an arc work?

The force-spring on an arc works by utilizing the principle of Hooke's Law, which states that the force exerted by a spring is directly proportional to the distance it is stretched or compressed. As the arc rotates, the spring stretches or compresses, generating a force on the attached mass. This force can cause the mass to accelerate in a circular motion.

## 3. What factors affect the force in a force-spring on an arc?

The force in a force-spring on an arc is affected by several factors, including the stiffness of the spring, the length of the arc, and the mass attached to the spring. A stiffer spring will exert a stronger force, a longer arc will result in a larger force due to the increased distance the spring can stretch or compress, and a heavier mass will require a greater force to accelerate.

## 4. What are some real-life applications of force-spring on an arc?

Force-spring on an arc systems have various real-life applications, including in mechanical devices such as clocks, watches, and suspension systems in vehicles. They are also used in science experiments to demonstrate the principles of circular motion and Hooke's Law.

## 5. How is the force in a force-spring on an arc calculated?

The force in a force-spring on an arc can be calculated using the equation F = -kx, where F is the force, k is the spring constant, and x is the distance the spring is stretched or compressed. The negative sign indicates that the force is in the opposite direction of the displacement of the spring. This equation follows Hooke's Law, which states that the force is directly proportional to the displacement.

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